A weak lensing_mass_reconstruction_of _the_large_scale_filament_massive_galaxy_cluster_macsj0717
Mon. Not. R. Astron. Soc. 000, 1–17 (XXXX) Printed 22 August 2012 (MN L TEX style ﬁle v2.2) A A Weak-Lensing Mass Reconstruction of the Large-Scale Filament Feeding the Massive Galaxy Cluster MACSJ0717.5+3745arXiv:1208.4323v1 [astro-ph.CO] 21 Aug 2012 Mathilde Jauzac,1,2⋆ Eric Jullo,1,3 Jean-Paul Kneib,1 Harald Ebeling,4 Alexie Leauthaud,5 Cheng-Jiun Ma,4 Marceau Limousin,1,6 Richard Massey,7 Johan Richard8 1 Laboratoire d’Astrophysique de Marseille - LAM, Universit´ d’Aix-Marseille & CNRS, UMR7326, 38 rue F. Joliot-Curie, 13388 Marseille Cedex 13, France e 2 Astrophysics and Cosmology Research Unit, School of Mathematical Sciences, University of KwaZulu-Natal, Durban 4041, South Africa 3 Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109, USA 4 Institute for Astronomy, University of Hawaii, 2680 Woodlawn Drive, Honolulu, Hawaii 96822, USA 5 Kavli Institute for the Physics and Mathematics of the Universe, Todai Institutes for Advanced Study, the University of Tokyo, Kashiwa, Japan 277-8583 (Kavli IPMU, WPI) 6 Dark Cosmology Centre, Niels Bohr Institute, University of Copenhagen, Juliane Maries Vej 30, DK-2100 Copenhagen, Denmark 7 Institute for Computational Cosmology, Durham University, South Road, Durham DH1 3LE, U.K. 8 CRAL, Observatoire de Lyon, Universit´ Lyon 1, 9 Avenue Ch. Andr´ , 69561 Saint Genis Laval Cedex, France e e Accepted 2012 August 20. Received 2012 August 15; in original form: 2012 April 27 ABSTRACT We report the ﬁrst weak-lensing detection of a large-scale ﬁlament funneling matter onto the core of the massive galaxy cluster MACSJ0717.5+3745. Our analysis is based on a mosaic of 18 multi-passband images obtained with the Ad- vanced Camera for Surveys aboard the Hubble Space Telescope, covering an area of ∼ 10×20 arcmin2 . We use a weak-lensing pipeline developed for the COSMOS survey, modiﬁed for the analysis of galaxy clusters, to produce a weak-lensing catalogue. A mass map is then com- puted by applying a weak-gravitational-lensing multi-scale reconstruction technique designed to describe irregular mass distributions such as the one investigated here. We test the result- ing mass map by comparing the mass distribution inferred for the cluster core with the one derived from strong-lensing constraints and ﬁnd excellent agreement. Our analysis detects the MACSJ0717.5+3745 ﬁlament within the 3 sigma detection con- tour of the lensing mass reconstruction, and underlines the importance of ﬁlaments for the- oretical and numerical models of the mass distribution in the Cosmic Web. We measure the ﬁlament’s projected length as ∼ 4.5 h−1 Mpc, and its mean density as (2.92±0.66)×108 h74 M⊙ 74 kpc−2 . Combined with the redshift distribution of galaxies obtained after an extensive spectro- scopic follow-up in the area, we can rule out any projection eﬀect resulting from the chance alignment on the sky of unrelated galaxy group-scale structures. Assuming plausible con- straints concerning the structure’s geometry based on its galaxy velocity ﬁeld, we construct a 3D model of the large-scale ﬁlament. Within this framework, we derive the three-dimensional length of the ﬁlament to be 18 h−1 Mpc. The ﬁlament’s deprojected density in terms of the 74 critical density of the Universe is measured as (206 ± 46) × ρcrit , a value that lies at the very high end of the range predicted by numerical simulations. Finally, we study the distribution of stellar mass in the ﬁeld of MACSJ0717.5+3749 and, adopting a mean mass-to-light ratio M∗ /LK of 0.73 ± 0.22 and assuming a Chabrier Initial-Mass Function, measure a stellar mass fraction along the ﬁlament of (0.9 ± 0.2)%, consistent with previous measurements in the vicinity of massive clusters. Key words: cosmology: observations - gravitational lensing - large-scale structure of Uni- verse 1 INTRODUCTION In a Universe dominated by Cold Dark Matter (CDM), such as ⋆ E-mail: email@example.com (MJ) the one parameterised by the ΛCDM concordance cosmology, hi-
2 M. Jauzac, E. Jullo, J.-P. Kneib, H. Ebeling, A. Leauthaud, C. J. Ma, M. Limousin, R. Massey, J. Richarderarchical structure formation causes massive galaxy clusters toform through a series of successive mergers of smaller clustersand groups of galaxies, as well as through continuous accretionof surrounding matter. N-body simulations of the dark-matter dis-tribution on very large scales (Bond et al. 1996; Yess & Shandarin1996; Arag´ n-Calvo et al. 2007; Hahn et al. 2007) predict that othese processes of merging and accretion occur along preferred di-rections, i.e., highly anisotropically. The result is the “cosmic web”(Bond et al. 1996), a spatially highly correlated structure of inter-connected ﬁlaments and vertices marked by massive galaxy clus-ters. Abundant observational support for this picture has been pro-vided by large-scale galaxy redshift surveys (e.g., Geller & Huchra1989; York et al. 2000; Colless et al. 2001) showing voids sur-rounded and connected by ﬁlaments and sheets of galaxies. A variety of methods have been developed to detect ﬁlamentsin surveys, among them a “friends of friends” algorithm (FOF,Huchra & Geller 1982) combined with “Shapeﬁnders” statistics(Sheth & Jain 2003); the “Skeleton” algorithm (Novikov et al.2006; Sousbie et al. 2006); a two-dimensional technique developedby Moody et al. (1983); and the Smoothed Hessian Major Axis Fil-ament Finder (SHMAFF, Bond et al. 2010). Figure 1. Area of our spectroscopic survey of MACSJ0717.5+3745. Out- Although ubiquitous in large-scale galaxy surveys, ﬁlaments lined in red is the region covered by our Keck/DEIMOS masks; outlinedhave proven hard to characterise physically, owing to their low in blue is the area observed with HST/ACS. Small circles correspond todensity and the fact that the best observational candidates often objects for which redshifts were obtained; large ﬁlled circles mark clusterturn out to be not primordial in nature but the result of recent members. The black contours show the projected galaxy density (see Ma etcluster mergers. Speciﬁcally, attempts to study the warm-hot in- al. 2008).tergalactic medium (WHIM, Cen & Ostriker 1999), resulting fromthe expected gravitational heating of the intergalactic medium inﬁlaments, remain largely inconclusive because it is hard to ascer- gaps between CCD chips. Indeed, Gavazzi et al. (2004) showedtain for ﬁlaments near cluster whether spectral X-ray features orig- the detection to have been spurious by means of a second studyinate from the ﬁlament or from past or ongoing clusters merg- of MS0302+17 using the CFHT12K camera. A weak gravitationalers (Kaastra et al. 2006; Rasmussen 2007; Galeazzi et al. 2009; lensing analysis with MPG/ESO Wide Field Imager conducted byWilliams et al. 2010). Some detections appear robust as they have Gray et al. (2002) claimed the detection of a ﬁlament in the triplebeen repeatedly conﬁrmed (Fang et al. 2002, 2007; Williams et al. cluster A901/902. The candidate ﬁlament appeared to connect two2007) but are based on just one X-ray line. An alternative observa- of the clusters and was detected in both the galaxy distribution andtional method is based on a search for ﬁlamentary overdensities of in the weak-lensing mass map. However, this detection too wasgalaxies relative to the background (Pimbblet & Drinkwater 2004; of low signiﬁcance and coincided partly with a gap between twoEbeling et al. 2004). When conducted in 3D, i.e., including spec- chips of the camera. As in the case of MS0302+17, a re-analysis oftroscopic galaxy redshifts, this method is well suited to detecting the A901/A902 complex using high-quality HST/ACS images byﬁlament candidates. It does, however, not allow the determination Heymans et al. (2008) failed to detect the ﬁlament and led the au-of key physical properties unless it is supplemented by follow-up thors to conclude that the earlier detection was caused by residualstudies targeting the presumed WHIM and dark matter which are PSF systematics and limitation of the KS93 mass reconstructionexpected to constitute the vast majority of the mass of large-scale used in the study by Gray et al. (2002). A further detection of aﬁlaments. By contrast, weak gravitational lensing oﬀers the tan- ﬁlament candidate was reported by Dietrich et al. (2005) based ontalising possibility of detecting directly the total mass content of a weak gravitational lensing analysis of the close double clusterﬁlaments (Mead et al. 2010), since the weak-lensing signal arises A222/A223. However, as in other similar cases, the proximity offrom luminous and dark matter alike, regardless of its dynamical the two clusters connected by the putative ﬁlament raises the pos-state. sibility of the latter being a merger remnant rather than primordial Previous weak gravitational lensing studies of binary clusters in nature.found tentative evidence of ﬁlaments, but did not result in clear de- In this paper we describe the ﬁrst weak gravitational analy-tections. One of the ﬁrst eﬀorts was made by Clowe et al. (1998) sis of the very massive cluster MACSJ0717.5+3745 (z = 0.55;who reported the detection of a ﬁlament apparently extending from Edge et al. 2003; Ebeling et al. 2004, 2007; Ma et al. 2008, 2009).the distant cluster RX J1716+67 (z = 0.81), using images obtained Optical and X-ray analyses of the system (Ebeling et al. 2004;with the Keck 10m telescope and University of Hawaii (UH) 2.2m Ma et al. 2008, 2009) ﬁnd compelling evidence of a ﬁlamentarytelescope. This ﬁlamentary structure would relate two distinct sub structure extending toward the South-East of the cluster core. Us-clusters detected on the mass and light maps. The detection was ing weak-lensing data to reconstruct the mass distribution in andnot conﬁrmed though. Almost at the same time Kaiser et al. (1998) around MACSJ0717.5+3745, we directly detect the reported ﬁla-conducted a weak lensing study of the supercluster MS0302+17 mentary structure in the ﬁeld of MACSJ0717.5+3745.with the UH8K CCD camera on the Canada France Hawaii Tele- The paper is organized as follows. After an overview ofscope (CFHT). Their claimed detection of a ﬁlament in the ﬁeld the observational data in Section 2, we discuss the gravitationalwas, however, questioned on the grounds that the putative ﬁla- lensing data in hand in Section 3. The modeling of the massment overlapped with both a foreground structure as well as with using a multi-scale approach is described in Section 4. Results are
The Large-Scale Filament Feeding MACSJ0717.5+3745 3Table 1. Overview of the HST/ACS observations of MACSJ0717.5+3745. *: Cluster core; observed through F555W, rather than F606W ﬁlter. F606W F814W R.A. (J2000) Dec (J2000) Date Exposure Time (s) Date Exposure Time (s) Programme ID 07 17 32.93 +37 45 05.4 2004-04-02* 4470* 2004-04-02 4560 9722 07 17 31.81 +37 49 20.6 2005-02-08 1980 2005-02-08 4020 10420 07 17 20.38 +37 47 07.5 2005-01-27 1980 2005-01-27 4020 10420 07 17 08.95 +37 44 54.3 2005-01-27 1980 2005-01-27 4020 10420 07 17 43.23 +37 47 03.1 2005-01-30 1980 2005-01-30 4020 10420 07 17 20.18 +37 42 38.8 2005-02-01 1980 2005-02-01 4020 10420 07 17 54.26 +37 44 49.3 2005-01-27 1980 2005-01-27 4020 10420 07 17 42.82 +37 42 36.3 2005-01-24 1980 2005-01-25 4020 10420 07 17 31.39 +37 40 23.3 2005-02-01 1980 2005-02-01 4020 10420 07 18 05.46 +37 42 33.6 2005-02-04 1980 2005-02-04 4020 10420 07 17 54.02 +37 40 20.6 2005-02-04 1980 2005-02-04 4020 10420 07 17 42.79 +37 38 05.7 2005-02-05 1980 2005-02-05 4020 10420 07 18 16.65 +37 40 17.7 2005-02-05 1980 2005-02-05 4020 10420 07 18 05.22 +37 38 04.9 2005-02-05 1980 2005-02-05 4020 10420 07 17 53.79 +37 35 52.0 2005-02-05 1980 2005-02-05 4020 10420 07 18 27.84 +37 38 01.9 2005-02-08 1980 2005-02-08 4020 10420 07 18 16.40 +37 35 49.1 2005-02-08 1980 2005-02-08 4020 10420 07 18 04.97 +37 33 36.2 2005-02-09 1980 2005-02-09 4020 10420discussed in Section 5, and we present our conclusions in Section 6. Table 2. Overview of groundbased imaging observations of MACSJ0717.5+3745.All our results use the ΛCDM concordance cosmology withΩM = 0.3, ΩΛ = 0.7, and a Hubble constant H0 = 74 km s−1 Mpc−1 ,hence 1” corresponds to 6.065 kpc at the redshift of the cluster. Subaru CFHTMagnitudes are quoted in the AB system. B V RC IC z’ u* J KS Exposure (hr) 0.4 0.6 0.8 0.4 0.5 1.9 1.8 1.7 Seeing (arcsec) 0.8 0.7 1.0 0.8 0.6 1.0 0.9 0.72 OBSERVATIONSThe MAssive Cluster Survey (MACS, Ebeling et al. 2001) was theﬁrst cluster survey to search exclusively for very massive clustersat moderate to high redshift. Covering over 20,000 deg2 and us-ing dedicated optical follow-up observations to identify faint X-ray sources detected in the ROSAT All-Sky Survey, MACS com-piled a sample of over 120 very X-ray luminous clusters at z > 0.3, February 9, 2005, with the ACS aboard HST (GO-10420, PI Ebel-thereby more than tripling the number of such systems previously ing). The 3×6 mosaic consists of images in the F606W and F814Wknown. The high-redshift MACS subsample (Ebeling et al. 2007) ﬁlters, observed for roughly 2.0 ks and 4.0 ks respectively (1 & 2comprises 12 clusters a z > 0.5. MACSJ0717.5+3745 is one of HST orbits). Only 17 of the 18 tiles of the mosaic were coveredthem. All 12 were observed with the ACIS-I imaging spectrograph though, since the core of the cluster had been observed already (seeonboard the Chandra X-ray Observatory. Moderately deep optical Tab. 1 for more details).images covering 30 × 27 arcmin2 were obtained in ﬁve passbands Charge Transfer Ineﬃciency (CTI), due to radiation damage(B, V, R, I, z′ ) with the SuprimeCam wide-ﬁeld imager on the of the ACS CCDs above the Earth’s atmosphere, creates spuriousSubaru 8.2m Telescope, and supplemented with u-band imaging trails behind objects in HST/ACS images. Since CTI aﬀects galaxyobtained with MegaCam on the Canada France Hawaii Telescope photometry, astrometry, and shape measurements, correcting the ef-(CFHT). Finally, the cores of all clusters in this MACS subsam- fect is critical for weak-lensing studies. We apply the algorithmple were observed with the Advanced Camera for Surveys (ACS) proposed by Massey et al. (2010) which operates on the raw dataonboard HST in two bands, F555W & F814W, for 4.5ks in both and returns individual electrons to the pixels from which they werebands, as part of programmes GO-09722 and GO-11560 (PI Ebel- erroneously dragged during readout. Image registration, geometricing). distortion corrections, sky subtraction, cosmic ray rejection, and the ﬁnal combination of the dithered images are then performed using the standard MULTIDRIZZLE routines (Koekemoer et al. 2002). MULTIDRIZZLE parameters are set to values optimised for pre-2.1 HST/ACS Wide-Field Imaging cise galaxy shape measurement (Rhodes et al. 2007), and outputA mosaic of images of MACSJ0717.5+3745 and the ﬁlamentary images created with a 0.03” pixel grid, compared to the native ACSstructure to the South-East was obtained between January 24 and pixel scale of 0.05”.
4 M. Jauzac, E. Jullo, J.-P. Kneib, H. Ebeling, A. Leauthaud, C. J. Ma, M. Limousin, R. Massey, J. Richard 4 BRI selection BRI Redshift Distribution All galaxies before BRI selection Foreground galaxies (zphot) 250 after BRI selection Cluster galaxies (zphot) Foreground & Cluster galaxies (zspec) 3 200 Number of galaxies MAGB −MAGRc 150 2 100 1 50 0 0.0 0.5 1.0 1.5 0.2 0.4 0.6 0.8 1.0 1.2 1.4 MAGRc − MAGIc zFigure 2. Colour-colour diagram (B−R vs R−I) for objects within the Figure 3. Redshift distribution of all galaxies with B, Rc , and Ic photometryHST/ACS mosaic of MACSJ0717.5+3745. Grey dots represent all objects from Subaru/SuprimeCam observations that have photometric or spectro-in the study area. Unlensed galaxies diluting the shear signal are marked by scopic redshifts (black histogram). The cyan histogram shows the redshiftdiﬀerent colours: galaxies spectroscopically conﬁrmed as cluster members distribution of galaxies classiﬁed as background objects using the BRI cri-or foreground galaxies (green); galaxies classiﬁed as foreground objects be- terion illustrated in Fig. 2.cause of their photometric redshifts (red); and galaxies classiﬁed as clustermembers via photometric redshifts (yellow). The solid black lines delin-eate the BRI colour-cut deﬁned for this work to mitigate shear dilution byunlensed galaxies. 2.3 Spectroscopic and Photometric Redshifts Spectroscopic observations of MACSJ0717.5+3745 (including the full length of the ﬁlament) were conducted between 2000 and 2008, mainly with the DEIMOS spectrograph on the Keck-II 10m tele- scope on Mauna Kea, supplemented by observations of the cluster2.2 Groundbased Imaging core region performed with the LRIS and GMOS spectrographs on Keck-I and Gemini-North, respectively. The DEIMOS instrumentMACSJ0717.5+3745 was observed in the B, V, Rc , Ic and z′ bands setup combined the 600ZD grating with the GC455 order-blockingwith the Suprime-Cam wide-ﬁeld camera on the Subaru 8.2m tele- ﬁlter and a central wavelength between 6300 and 7000 Å; the expo-scope (Miyazaki et al. 2002). These observations are supplemented sure time per MOS (multi-object spectroscopy) mask was typicallyby images in the u* band obtained with the MegaPrime camera on 3×1800 s. A total of 18 MOS masks were used in our DEIMOSthe CFHT 3.6m telescope, as well as near-infrared imaging in the observations; spectra of 1752 unique objects were obtained (65 ofJ and KS bands obtained with WIRcam on CFHT. Exposure times them with LRIS, and 48 with GMOS), yielding 1079 redshifts, 537and seeing conditions for these observations are listed in Tab. 2 of them of cluster members. Figure 1 shows the area covered by(see also C.-J. Ma, Ph.D. thesis). All data were reduced using stan- our spectroscopic survey as well as the loci of the targeted galax-dard techniques which were, however, adapted to deal with special ies. The data were reduced with the DEIMOS pipeline developedcharacteristics of the Suprime-Cam and MegaPrime data; for more by the DEEP2 project.details see Donovan (2007). Photometric redshifts for galaxies with mRc <24.0 were com- The groundbased imaging data thus obtained are used primar- puted using the adaptive SED-ﬁtting code Le Phare (Arnouts et al.ily to compute photometric redshifts which allow the elimination 1999; Ilbert et al. 2006, 2009). In addition to employing χ2 opti-of cluster members and foreground galaxies that would otherwise mization during SED ﬁtting, Le Phare adaptively adjusts the pho-dilute the shear signal. To this end we use the object catalogue com- tometric zero points by using galaxies with spectroscopic redshiftspiled by Ma et al. (2008) which we describe brieﬂy in the follow- as a training set. This approach reduces the fraction of catastrophicing. Imaging data from the passbands listed in Tab. 2 were seeing- errors and also mitigates systematic trends in the diﬀerences be-matched using the technique described in Kartaltepe et al. (2008) tween spectroscopic and photometric redshifts (Ilbert et al. 2006).in order to allow a robust estimate of the spectral energy distribu- Further details, e.g. concerning the selection of targets fortion (SED) for all objects within the ﬁeld of view. The object cata- spectroscopy or the spectral templates used for the determinationlogue was then created using the SExtractor photometry package of photometric redshifts, are provided by Ma et al. (2008). The full(Bertin & Arnouts 1996) in ”dual mode” using the R-band image as redshift catalogue as well as an analysis of cluster substructure andthe reference detection image. More details are given in Ma et al. dynamics as revealed by radial velocities will be presented in Ebel-(2008). ing et al. (2012, in preparation).
The Large-Scale Filament Feeding MACSJ0717.5+3745 5 3.0 uBV selection uBV Redshift Distribution All galaxies before uBV selection Foregound galaxies (zphot) 250 after uBV selection Cluster galaxies (zphot) 2.5 Foreground & Cluster galaxies (zspec) 200 2.0 Number of galaxies MAGB −MAGV 150 1.5 100 1.0 0.5 50 0.0 0 −0.5 0.0 0.5 1.0 1.5 0.2 0.4 0.6 0.8 1.0 1.2 1.4 MAGu − MAGB zFigure 4. As Fig. 2 but for the B−V and u−B colours. The solid black Figure 5. Redshift distribution of all galaxies with u, B, and V photome-line delineates the uBV colour-cut deﬁned for this work to mitigate shear try from CFHT/MegaCam and Subaru/SuprimeCam observations that havedilution by unlensed galaxies. photometric or spectroscopic redshifts (black histogram). The cyan his- togram shows the redshift distribution of galaxies classiﬁed as background objects using the uBV criterion illustrated in Fig. 4.3 WEAK GRAVITATIONAL LENSING ANALYSIS3.1 The ACS catalogue all quantities derived from it. Identifying and eliminating as manyOur weak-lensing analysis is based on shape measurements in the of the contaminating unlensed galaxies is thus critical.ACS/F814W band. Following a method developed for the anal- As a ﬁrst step, we identify cluster galaxies with the helpysis of data obtained for the COSMOS survey and described in of the catalogue of photometric and spectroscopic redshifts com-Leauthaud et al. (2007) (hereafter L07) we use the SExtractor piled by Ma et al. (2008) from groundbased observations of thephotometry package (Bertin & Arnouts 1996) to detect sources in MACSJ0717.5+3745 ﬁeld; the limiting magnitude of this cata-our ACS imaging data in a two-step process. Called the “Hot-Cold” logue is mRc = 24. According to Ma & Ebeling (2010), all galaxiestechnique (Rix et al. 2004, L07), it consists of running SExtractor with spectroscopic redshifts 0.522 < zspec < 0.566 and with photo-twice: ﬁrst with a conﬁguration optimised for the detection of only metric redshifts 0.48 < z phot < 0.61 can be considered to be clusterthe brightest objects (the “cold” step), then a second time with a galaxies. An additional criterion can be deﬁned using the photomet-conﬁguration optimised for the detection of the faint objects (the ric redshifts derived as described in Sect. 2.3. Taking into account“hot” step) that contain most of the lensing signal. The resulting the statistical uncertainty of ∆z = 0.021 of the photometric red-object catalogue is then cleaned by removing spurious or duplicate shifts, galaxies are deﬁned as cluster members if their photometricdetections using a semi-automatic algorithm that deﬁnes polygonal redshift satisﬁes the criterion:masks around stars or saturated pixels. |z phot − zcluster | < σ phot−z , Star-galaxy classiﬁcation is performed by examining the dis-tribution of objects in the magnitude (MAG AUTO) vs peak withsurface-brightness (MU MAX) plane. This diagram allows us toseparate three classes of objects: galaxies, stars, and any remaining σ phot−z = (1 + zcluster )∆z = 0.036,spurious detections (i.e., artifacts, hot pixels and residual cosmic where z phot and zcluster are the photometric redshift of the galaxyrays). Finally, the drizzling process introduces pattern-dependent and the spectroscopic redshift of the galaxy cluster respectively.correlations between neighbouring pixels which artiﬁcially reduces Reﬂecting the need for a balance between completeness and con-the noise level of co-added drizzled images. We apply the remedy tamination, these redshift limits are much more generous than thoseused by L07 by simply scaling up the noise level in each pixel by used in conjunction with spectroscopic redshifts, which set the red-the same constant FA ≈ 0.316, deﬁned by Casertano et al. (2000). shift range for cluster membership to 3σ ∼ 0.0122. For more details, see C.-J. Ma (Ph.D. thesis), as well as Ma et al. (2008); Ma & Ebeling (2010).3.2 Foreground, Cluster & Background Galaxy In spite of these cuts according to galaxy redshift, the remain- Identiﬁcations ing ACS galaxy sample is most likely still contaminated by fore-Since only galaxies behind the cluster are gravitationally lensed, the ground and cluster galaxies, the primary reason being the largepresence of cluster members and foreground galaxies in our ACS diﬀerence in angular resolution and depth between the ACS andcatalogue dilutes the observed shear and reduces the signiﬁcance of Subaru images. The relatively low resolution of the groundbased
6 M. Jauzac, E. Jullo, J.-P. Kneib, H. Ebeling, A. Leauthaud, C. J. Ma, M. Limousin, R. Massey, J. Richarddata causes the Subaru catalogue to be confusion limited and makes the lens-source system. The convergence κ is deﬁned as the dimen-matching galaxies between the two catalogues diﬃcult, especially sionless surface mass density of the lens:near the cluster core. As a result, we can assign a redshift to only 1 2 Σ(DOL θ)∼ 15% of the galaxies in the HST/ACS galaxy catalogue. κ(θ) = ∇ ϕ(θ) = , (1) 2 Σcrit For galaxies without redshifts, we use colour-colour diagrams(B−R vs R−I, Fig. 2, and B−V vs u−B, Fig. 4) to identify fore- where θ is the angular position of the background galaxy, ϕ is theground and cluster members. Using galaxies with spectroscopic or deﬂection potential, Σ(DOL θ) is the physical surface mass densityphotometric redshifts from the full photometric Subaru catalogue of the lens, and Σcrit is the critical surface mass density deﬁned aswith a magnitude limit of mRc = 25, we identify regions marked c2 DOSdominated by unlensed galaxies (foreground galaxies and cluster Σcrit = . 4πGDOL DLSmembers). In the BRI plane we ﬁnd B−R < 2.6 (R−I) + 0.05;(R−I) > 1.03; or (B−R) < 0.9 to best isolate unlensed galaxies; in Here, DOL , DOS , and DLS represent the angular distances from thethe UBV plane the most eﬃcient criterion is B−V < −0.5 (u−B) + observer to the lens, from the observer to the source, and from the0.85. lens to the source, respectively. Figures 3 and 5 show the galaxy redshift distributions before Considering the shear γ as a complex number, we deﬁneand after the colour-colour cuts (BRI or uBV) are applied. The re- γ = γ1 + iγ2 ,sults of either kind of ﬁltering are similar. The uBV selection ismore eﬃcient at removing cluster members and foreground galax- where γ1 = |γ| cos 2φ and γ2 = |γ| sin 2φ are the two components ofies at z 0.6 (20% remain compared to 30% for the BRI criterion) the shear, γ, deﬁned previously, and φ is the orientation angle. Withbut also erroneously eliminates part of the background galaxy pop- this deﬁnition, the shear is deﬁned in terms of the derivatives of theulation. Comparing the convergence maps for both colour-colour deﬂection potential as :selection schemes, we ﬁnd the uBV selection to yield a better de- 1tection of structures in the area surrounding the cluster, indicating γ1 = (ϕ11 − ϕ22 ),that suppressing contamination by unlensed galaxies is more im- 2portant than a moderate loss of background galaxies from our ﬁnal γ2 = ϕ12 = ϕ21 ,catalogue (see Sect. 5 for more details). Since the redshift distribution of the background population withpeaks at 0.61 < z < 0.70 (cyan curve in Fig. 5) we assign, in the ∂2mass modelling phase, a redshift z = 0.65 to background galaxies ϕi j = ϕ(θ), i, j ∈ (1, 2). ∂θi ∂θ jwithout redshift. Following Kaiser & Squires (1993), the complex shear is re- lated to the convergence by:3.3 Shape measurements of Galaxies & Lensing Cuts 1 κ(θ) = − d2 θ′ Re[D(θ − θ′ )γ∗ (θ′ )].3.3.1 Theoretical Weak Gravitational Lensing Background πThe shear signal contained in the shapes of lensed background Here D(θ) is the complex kernel, deﬁned asgalaxies is induced by a given foreground mass distribution. In the 2 2 θ1 − θ2 + 2iθ1 θ2weak-lensing regime this shear is observed as a statistical deforma- D(θ) = ,tion of background sources. The observed shape of a source galaxy, |θ|4ε, is directly related to the lensing-induced shear, γ, according to and Re(x) deﬁnes the real part of the complex number x. The aster-the relation : isk denotes complex conjugation. The last equation shows that the surface mass density κ(θ) of the lens can be reconstructed straight- ε = εintrinsic + εlensing , forwardly if the shear γ(θ) caused by the deﬂector can be measuredwhere εintrinsic is the intrinsic shape of the source galaxy (which locally as a function of the angular position θ.would be observed in the absence of gravitational lensing), and γ εlensing = . 3.3.2 The RRG method 1−κHere κ is the convergence. In the weak-lensing regime, κ ≪ 1, To measure the shape of galaxies we use the RRG methodwhich reduces the relation between the intrinsic and the observed (Rhodes et al. 2000) and the pipeline developed by L07. Havingshape of a source galaxy to been developed for the analysis of data obtained from space, the RRG method is ideally suited for use with a small, diﬀraction- ε = εintrinsic + γ. limited PSF as it decreases the noise on the shear estimators byAssuming galaxies are randomly oriented on the sky, the ellipticity correcting each moment of the PSF linearly, and only dividing themof galaxies is an unbiased estimator of the shear, down to a limit at the very end to compute an ellipticity.referred to as “intrinsic shape noise”, σintrinsic (for more details see The ACS PSF is not as stable as one might expect from aL07; Leauthaud et al. 2010, hereafter L10). Unavoidable errors in space-based camera. Rhodes et al. (2007) showed that both the sizethe galaxy shape measurement are accounted for by adding them in and the ellipticity pattern of the PSF varies considerably on timequadrature to the“intrinsic shape noise”: scales of weeks due to telescope ’breathing’. The thermal expan- sion and contraction of the telescope alter the distance between the σ2 = σ2 γ 2 measurement + σintrinsic . primary and the secondary mirrors, inducing a deviation of the ef- The shear signal induced on a background source by a given fective focus and thus from the nominal PSF which becomes largerforeground mass distribution will depend on the conﬁguration of and more elliptical. Using version 6.3 of the TinyTim ray-tracing
The Large-Scale Filament Feeding MACSJ0717.5+3745 7program, Rhodes et al. (2007) created a grid of simulated PSF im- In order to optimize the signal-to-noise ratio, we introduce anages at varying focus oﬀsets. By comparing the ellipticity of ∼ inverse-variance weighting scheme following L10:20 stars in each image to these models, Rhodes et al. (2007) wereable to determine the eﬀective focus of the images. Tests of this 1 wγ = ˜ .algorithm on ACS/WFC images of dense stellar ﬁelds conﬁrmed σ2 γ ˜that the best-ﬁt eﬀective focus can be repeatedly determined froma random sample of 10 stars brighter than mF814W = 23 with an Hence faint small galaxies which have large measurement errorsrms error of 1µm. Once images have been grouped by their eﬀec- are down-weighted with respect to sources that have well measuredtive focus position, the few stars in each images can be combined shapes.into one large catalog. PSF parameters are then interpolated usinga polynomial ﬁt in the usual weak-lensing fashion (Massey et al.2002). More details on the PSF modelling scheme are given inRhodes et al. (2007). 3.3.4 Lensing Cuts The RRG method returns three parameters: d, a measure of thegalaxy size, and, the ellipticity represented by the vector e = (e1 , e2 ) The last step in constructing the weak-lensing catalogue for thedeﬁned as follows: MACSJ0717.5+3745 ﬁeld consists of applying lensing cuts, i.e., to exclude galaxies whose shape parameters are ill-determined and a2 − b2 will increase the noise in the shear measurement more than they add e = a2 + b2 to the shear signal. However, in doing so, we need to take care note1 = e cos(2φ) to introduce any biases. We use three galaxy properties to establishe2 = e sin(2φ), the following selection criteria:where a and b are the half-major and half-minor axis of the back- • Their estimated detection signiﬁcance:ground galaxy, respectively, and φ is the orientation angle of theellipse deﬁned previously. The ellipticity e is then calibrated by a S FLUX AUT O = > 4.5;factor called shear polarizability, G, to obtain the shear estimator γ: ˜ N FLUXERR AUT O e where FLUX AUTO and FLUXERR AUTO are parameters re-γ=C˜ . (2) G turned by SExtractor;The shear susceptibility factor G is measured from moments of the • Their total ellipticity:global distribution of e and other shape parameters of higher or-der (see Rhodes et al. 2000). The Shear TEsting Program (STEP; e= e2 + e2 < 1; 1 2Massey et al. 2007) for COSMOS images showed that G is not con-stant but varies as a function of redshift and S/N. To determine G • Their size as deﬁned by the RRG d parameter:for our galaxy sample we use the same deﬁnition as the one usedfor the COSMOS weak-lensing catalogue (see L07): d > 0.13′′ . S /N − 17 G = 1.125 + 0.04 arctan . The requirement that the galaxy ellipticity be less than unity 4 may appear trivial and superﬂuous. In practice it is meaningfulFinally, C, in Eq. 2 is the calibration factor. It was determined though since the RRG method allows measured ellipticity valuesusing a set of simulated images similar to those used by STEP to be greater than 1 because of noise, although ellipticity is by def-(Heymans et al. 2006; Massey et al. 2006) for COSMOS images, inition restricted to e 1. Because Lenstool prevents ellipticitiesand is given by C = (0.86−0.05 )−1 (for more details see L07). +0.07 to be larger than 1, we removed the 251 objects with an ellipticity greater than unity from the RRG catalogue (2% of the catalogue). Serving a similar purpose, the restriction in the RRG size parameter3.3.3 Error of the Shear Estimator d aims to eliminate sources with uncertain shapes. PSF corrections become increasingly signiﬁcant as the size of a galaxy approachesAs explained in Sect. 3.3.1, the uncertainty in our shear estimator that of the PSF, making the intrinsic shape of a galaxy diﬃcult tois a combination of intrinsic shape noise and shape measurement measure.error: Our ﬁnal weak-lensing catalogue is composed of 10170 back- σ2 = σ2 2 ground galaxies, corresponding to a density of ∼ 52 galaxies γ ˜ intrinsic + σmeasurement , arcmin−2 . In addition to applying the aforementioned cuts, and in 2where σγ is referred to as shape noise. The shape measurement ˜ order to ensure an unbiased mass reconstruction in the weak lens-error is determined for each galaxy as a function of size and mag- ing regime only, we also remove all background galaxies locatednitude. Applying the method implemented in the PHOTO pipeline in the multiple-image (strong-lensing) region deﬁned by an ellipse(Lupton et al. 2001) to analyze data from the Sloan Digital Sky Sur- aligned with the cluster elongation and with a semi-major axis ofvey, we assume that the optical moments of each object are the 55”, a semi-minor axis of 33”. From the resulting mass-map pre-same as the moments computed for a best-ﬁt Gaussian. Since the sented in Sect. 5, we a-posteriori derived a convergence histogramellipticity components (which are uncorrelated) are derived from of the pixels outside this region, and found that 90% of them arethe moments, the variances of the ellipticity components can be smaller than κ = 0.1, with a mean value of κ = 0.03. The shearobtained by linearly propagating the covariance matrix of the mo- and convergence are so weak because the ratio DLS /DOS = 0.14ments. The value of the intrinsic shape noise, σintrinsic , is taken to be for background galaxies at redshift zmed = 0.65 and the cluster at0.27 (for more details see L07, L10). z = 0.54 (see Sect. 4).
8 M. Jauzac, E. Jullo, J.-P. Kneib, H. Ebeling, A. Leauthaud, C. J. Ma, M. Limousin, R. Massey, J. Richard4 MASS DISTRIBUTIONThe mass modelling for the entire MACSJ0717.5+3745 ﬁeld isperformed using the LENSTOOL1 (Jullo et al. 2007) software, us-ing the adaptive-grid technique developed by Jullo & Kneib (2009)and modiﬁed by us for weak-lensing mass measurements. BecauseLENSTOOL implements a Bayesian sampler, it provides manymass maps ﬁtting the data that can be used to obtain a mean massmap and to determine its error.4.1 Multi-Scale Grid MethodWe start with the method proposed by Jullo & Kneib (2009) tomodel the cluster mass distribution using gravitational lensing. This Figure 6. Distribution of grid nodes and galaxy-scale potentials, superim-recipe uses a multi-scale grid of Radial Basis Functions (RBFs) posed on the K-band light map of MACSJ0717.5+3745. Cyan crosses rep-with physically motivated proﬁles and lensing properties. With a resent the location of 468 RBFs at the nodes of the multi-scale grid; magentaminimal number of parameters, the grid of RBFs of diﬀerent sizes circles represent galaxy-scale potentials used to describe the contribution ofprovides higher resolution and sharper contrast in regions of higher individual cluster members. The white dashed line deﬁnes the HST/ACSdensity where the number of constraints is generally higher. It is ﬁeld of view. The white cross marks the cluster centre at 07:17:30.025, +37:45:18.58 (R.A., Dec).well suited to describe irregular mass distributions like the one in-vestigated here. The initial multi-scale grid is created from a smoothed map Jullo & Kneib (2009) found to yield an optimal compromise be-of the cluster K-band light and is recursively reﬁned in the densest tween model ﬂexibility and overﬁtting. We then adapt the techniqueregions. In the case of MACSJ0717.5+3745, this method is fully proposed by Diego et al. (2007) to our multiscale grid model to ﬁtadaptive as we want to sample a wide range of masses, from the the weak-lensing data (κ ≪ 1). Assuming a set of M images and acluster core to the far edge of the HST/ACS ﬁeld where the ﬁl- i model comprised of N RBFs, the relation between the weights σ2 0amentary structure is least dense. Initially, the ﬁeld of interest is and the 2M components of the shear is given bylimited to a hexagon, centred on the cluster core and split into sixequilateral triangles (see Fig. 1 in Jullo & Kneib 2009). This initial (1,1) ∆(1,N) 1 ··· grid is subsequently reﬁned by applying a splitting criterion that is γ1 ∆1 1 . . based on the surface density of the light map. Hence, a triangle will . . . .. . . . . σ2 1 . be split into four smaller triangles if it contains a single pixel that (M,1) M γ (M,N) 0 ∆ ··· ∆1 1 1 . exceeds a predeﬁned light-surface-density threshold. . = (1,1) . ∆(1,N) 1 γ ∆ ··· Once the adaptive grid is set up, RBFs described by Trun- 2 2 2 . 2N σ . . cated Isothermal Mass Distributions (TIMD), circular versions . . .. . 0 . . . . of truncated Pseudo Isothermal Elliptical Mass Distributions M (1,M) (M,N) γ2 ∆2 ··· ∆2(PIEMD) (see, e.g., Kassiola & Kovner 1993; Kneib et al. 1996;Limousin et al. 2005; El´asd´ ttir et al. 2007) are placed at the grid ı o withnode locations. The analytical expression of the TIMD mass sur- DiLS (i, j)face density is given by ∆(i, j) = 1 γ , DiOS 1 2 Σ(R) = σ0 f (R, rcore , rcut ) DiLS (i, j)with ∆(i, j) = 2 γ , DiOS 2 1 rcut 1 1 f (R, rcore , rcut ) = − . where 2G rcut − rcore rcore + R2 2 2 rcut +R 2 1 γ1 j) = (i, (∂11 Φ j (Ri j ) − ∂22 Φi (Ri j )), 2 Hence, f deﬁnes the proﬁle, and σ2 deﬁnes the weight of the 0RBF. This proﬁle is characterized by two changes in slope at ra- γ2 j) = ∂12 Φ j (Ri j ) = ∂21 Φ j (Ri j ), (i,dius values of rcore and rcut . Within rcore , the surface density is ap-proximately constant, between rcore and rcut , it is isothermal (i.e., andΣ ∝ r−1 ), and beyond rcut it falls as Σ ∝ r−3 . This proﬁle is physi- Ri j = |θi − θ j |.cally motivated and meets the three important criteria of a) featur-ing a ﬁnite total mass, b) featuring a ﬁnite central density, and c) In the above, DiLS and DiOS are the angular distances from thebeing capable of describing extended ﬂat regions, in particular in RBF j to the background source i and from the observer to thethe centre of clusters. background source i, respectively, and Φ is the projected gravita- The RBFs’ rcore value is set to the size of the smallest nearby tional potential. γk=1,2 are the two components of the shear, ∆(i, j) k=1,2triangle, and their rcut parameter is set to 3rcore , a scaling that j is the value of the RBF normalized with σ2 = 1, centered on the 0 grid node located at θ j , and computed at a radius R = |θi − θ j |. The contribution of this RBF to the predicted shear at location θi is j1 LENSTOOL is available online: http://lamwws.oamp.fr/lenstool given by the product ∆(i, j) σ2 (see Eq. 1). More details about this k=1,2 0
The Large-Scale Filament Feeding MACSJ0717.5+3745 9method will be provided in a forthcoming paper (Jullo et al. 2012,in preparation). Figure 6 shows the distribution of the 468 RBFs superimposedon the light map used to deﬁne the multi-scale grid. The smallestRBF has a rcore = 26′′ . Note that although Lenstool can performstrong lensing, and reduced-shear optimization, here the proposedformalism assumes weak-shear with κ ≪ 1. To get an unbiased es-timator, we remove the background galaxies near the cluster corefrom the catalogue, but we keep RBFs in this region as we found itimproves the mass reconstruction. In order to check our weak-shearassumption, we multiply the resulting convergence map by the fac-tor 1 − κ, and ﬁnd this minor correction only represents about 5% at300 kpc and less than 1% at 500 kpc. It conﬁrms that working witha weak-shear assumption in this case is not biasing our results. On Figure 7. Contours of the convergence κ in the MACS0717.5+3745 ﬁeldFig. 8, the black dashed curve corresponds to the corrected weak- obtained using the inversion method described by Seitz & Schneider (1995),shear optimization, while the black curve represents the weak-shear overlaid on the K-band light map. Magenta contours represent the 1, 2 andoptimization proﬁle. Both shows a really good agreement with the 3σ contours. Cyan crosses mark the position of two galaxy groups (see textstrong-lensing results (magenta curve). for details). The white cross marks again the cluster centre (cf. Fig. 6). 4.3 Mass Modeling4.2 Cluster Member Galaxies The mass reconstruction is conducted using LENSTOOL whichOur catalogue of cluster members is compiled from the photomet- implements an optimisation method based on a Bayesian Markovric catalogue of Ma et al. (2008). Within the HST/ACS study area Chain Monte Carlo (MCMC) approach (Jullo et al. 2007). Wewe identify as cluster members 1244 galaxies with spectroscopic chose this approach because we want to propagate as transparentlyand/or photometric redshifts within the redshift ranges deﬁned in as possible errors on the ellipticity into errors on the ﬁlament massSect. 3.2. We use these galaxies’ KS -band luminosities as mass es- measurement. This method provides two levels of inference: pa-timators (see below for details). rameter space exploration and model comparison, by means of the All cluster members are included in the lens model in the form posterior Probability Density Function (PDF) and the Bayesian ev-of truncated PIEMD potentials (see Sect. 4.1) with characteristic idence, respectively.properties scaled according to their K-band luminosity: All of these quantities are related by the Bayes Theorem: 1/2 Pr(D|θ, M)Pr(θ|M) ∗ L Pr(θ|D, M) ∝ , rcore = rcore , Pr(D|M) L∗ where Pr(θ|D, M) is the posterior PDF, Pr(D|θ, M) is the likelihood L 1/2 of a realisation yielding the observed data D given the parameters ∗ rcut = rcut , θ of the model M, and, Pr(θ|M) is the prior PDF for the parame- L∗ ters. Pr(D|M) is the probability of obtaining the observed data Dand, given the assumed model M, also called the Bayesian evidence. It 1/4 measures the complexity of the model. The posterior PDF will be L σ0 = σ∗ 0 . the highest for the set of parameters θ that yields the best ﬁt and L∗ is consistent with the prior PDF. Jullo et al. (2007) implemented an These scaling relations are found to well describe early- annealed Markov Chain to converge progressively from the priortype cluster galaxies (e.g. Wuyts et al. 2004; Fritz et al. 2005) un- PDF to the posterior PDF.der the assumptions of mass tracing light and the validity of the For the weak-lensing mass mapping, we implement an addi-Faber & Jackson (1976) relation. Since the mass, M, is propor- tional level of complexity based on the Gibbs sampling techniquetional to σ2 rcut , the above relations ensure M ∝ L, assuming that 0 (see Massive Inference in the Bayesys manual, Skilling 1998). Ba-the mass-to-light ratio is constant for all cluster members. sically, only the posterior distribution of the most relevant RBFs is To ﬁnd suitable values of rcore , rcut , and σ∗ we take advantage ∗ ∗ explored. The number of RBFs to explore is an additional free pa- 0of the results of the strong-lensing analysis of MACSJ0717.5+3745 rameter with a Poisson prior. Exploring possible values of this priorrecently conducted by Limousin et al. (2012). Their mass model of in simulations, we ﬁnd that the input mass is well recovered whenthe cluster also included cluster members, using the scaling rela- the mean of this prior is set to 2% of the total number of RBFs in itions deﬁned above (see also Limousin et al. 2007). For a given L∗ the model. The weights of the RBFs, σ2 , are decomposed into the 0luminosity, given by m∗ = 19.16, the mean apparent magnitude of product of a quantum element of weight, q, common to all RBF,a cluster member in K-band, Limousin et al. (2012) set all geomet- and a multiplicative factor ζ i . In order to have positive masses, werical galaxy parameters (centre, ellipticity, position angle) to the make ζ follow a Poisson prior (case MassInf=1), and q to follow ∗values measured with SExtractor, ﬁxed rcore at 0.3 kpc, and then the prior distribution π(q) = q−2 q exp−q/q0 , and we ﬁx the initial 0 ∗ ∗ isearched for the values of σ0 and rcut that yield the best ﬁt. We here guess q0 = 10 km2 /s2 . The ﬁnal distribution of σ2 is well approxi- 0 ∗ ∗use the same best-ﬁt values, rcut = 60 kpc and σ0 = 163 kpc/s, to mated by a distribution π(q) with q0 = 12 km2 /s2 , and, we ﬁnd thatdeﬁne the potentials of the cluster members. Hence, all parameters 16.8 ± 4.8 RBFs are necessary on average to reconstruct the massdescribing cluster members are ﬁxed in our model; their positions distribution given our data, i.e. about 3.5% of the total number ofare marked by the magenta circles in Fig. 6. RBFs in the model. This new algorithm is fast, as it can deliver a
10 M. Jauzac, E. Jullo, J.-P. Kneib, H. Ebeling, A. Leauthaud, C. J. Ma, M. Limousin, R. Massey, J. Richard Figure 9. Mass distribution in the core of MACSJ0717.5+3745. Cyan con- tours represent the mass distribution inferred in the strong-lensing study by Limousin et al. (2012); white contours show the mass distribution obtained by our weak-lensing analysis; and magenta contours represent the distribu- tion of the cluster K-band light. The orange cross marks the cluster center adopted in the analysis (cf. Fig. 6). mic Bayesian evidence is then given byFigure 8. Density proﬁles within the core of MACSJ0717.5+3749. The ma-genta curve represents strong-lensing results from Limousin et al. (2012); 1 1the black curve shows the proﬁle derived from our weak-lensing analysis; log(E) = − χ2 λ dλ 2 0the black dashed curve shows the weak-lensing proﬁle corrected from theweak-shear approximation where the average is computed over a set of 10 MCMC realizations at any given iteration step λi , and the integration is performed over. The grey area marks the region within which multiple images are observed. all iterations λi from the initial model (λ = 0) to the best-ﬁt result (λ = 1). An increment in dλ depends on the variance between the 10 likelihoods computed at a given iteration, and a convergencemass map in 20 minutes for about 10,000 galaxies and 468 RBFs rate that we set equal to 0.1 (see Bayesys manual for details). The— the previous algorithm used in Jullo & Kneib (2009) was taking increment gets larger as the algorithm converges towards 1.more than 4 weeks to converge. The new algorithm has been testedin parallel on ﬁve processors clocked at 2 GHz. We deﬁne the likelihood function as (see e.g. Schneider et al. 5 RESULTS(2000): 5.1 Kappa Map : Standard mass reconstruction 1 χ2 Pr(D|θ) = exp (− ), We test our catalogue of background galaxies by mapping the con- ZL 2 vergence κ in the MACSJ0717.5+3745 ﬁeld. We use the methodwhere D is the vector of ellipticity component values, and θ is a described in Sect. 3.3.1, which is based on the inversion equa-vector of the free parameters σ2 . χ2 is the usual goodness-of-ﬁt i tion found by Kaiser & Squires (1993) and developed further bystatistic: Seitz & Schneider (1995). It shows that the best density recon- M 2 structions are obtained when the smoothing scale is adapted to the (˜ j,i − 2γ j,i (θi ))2 γχ2 = . (3) strength of the signal. We ﬁnd a smoothing scale of 3 arcmin to i=1 j=1 σ2 γ˜ provide a good compromise between signal-to-noise considerations and map resolution. We estimate the noise directly from the mea-The 2M intrinsic ellipticity components (M is the number of back- sured errors, σmeasurement , averaged within the grid cells.ground sources), are deﬁned as follows: The resulting κ-map is shown in Fig. 7, overlaid on a smoothedεintrinsic, j = γ j (θ j ) − 2γ j (θ j ) ˜ (4) image of the K-band light from cluster galaxies. We identify two substructures south-east of the cluster core whose locations matchand, are assumed to have been drawn from a Gaussian distribution the extent of the ﬁlamentary structure seen in the galaxy distribu-with variance deﬁned in Sect. 3.3.1 : tion. The ﬁrst of these, near the cluster core, coincides with the beginning of the optical ﬁlament; the second falls close to the ap- σ2 = σ2 γ ˜ 2 intrinsic + σmeasure . parent end of the ﬁlament close to the edge of our study area. AThe normalization factor is given by simple inversion technique thus already yields a 2 sigma detections of parts of the ﬁlament. M √ The Chandra observation of MACS0717.5+3745 shows X- ZL = 2π σγi . ˜ ray detections of two satellite groups of galaxies embedded in the i=1 ﬁlament (private communication H. Ebeling, see also Fig. 1 of Note the factor of 2 in Eqn. 3 and 4 because of the particular Ma et al. 2009, and Fig. 10 of this paper). Their X-ray coordinatesdeﬁnition of the ellipticity in RRG (see Sect. 3.3.2). The logarith- (R.A., Dec, J2000) are : i) 07:17:53.618, +37:42:10.46, and, ii)
The Large-Scale Filament Feeding MACSJ0717.5+3745 11Figure 10. Mass map from our weak-gravitational lensing analysis overlaid on the light map of the mosaic. The two sets of contours show the X-ray surfacebrightness (cyan), and weak-lensing mass (white). The bold white contour corresponds to a density of 1.84 × 108 h74 M⊙ .kpc−2 . The orange cross marks thelocation of the ﬁducial cluster centre, and the two blue crosses show the positions of the two X-ray detected satellite groups mentioned in Sect. 5.1. The dashedcyan lines delineates the edges of the Chandra/ACIS-I ﬁeld of view. The yellow box, ﬁnally, marks the cluster core region shown in Fig. 9. The magenta lineemphasises the extent and direction of the large-scale ﬁlament.07:18:19.074, +37:41:13.14 (cyan crosses in Fig. 7). The ﬁrst of the cluster centre because it marks the barycenter of the Einsteinthese, close to the ﬁlament-cluster interface, is detected by the in- ring measured by Meneghetti et al. (2011). Another SL analysis ofversion technique, but not the second. Conversely, the peak in the MACSJ0717.5+3745 was performed by Zitrin et al. (2009) who re-convergence map in the southeastern corner of our study area is not port a mass of MSL (R < 350 kpc) = (7.0 ± 0.5) 1014 h−1 M⊙ . 74detected in X-rays. Figure 8 compares the mass density proﬁles derived from the SL analysis (magenta line) and from our WL analysis (black line); note the very good agreement. The WL density proﬁle has been cut5.2 Mass Map : Iterative mass reconstruction up to ∼300 kpc as this region corresponds to the multiple-image regime, therefore does not contain any WL constraints.The primary goal of this paper is the detection of the large-scale In Fig. 8, the SL density proﬁle is extrapolated beyond theﬁlament with weak-lensing techniques and the characterisation of multiple-image region (the cluster core), while the WL densityits mass content. To calibrate the mass map of the entire structure proﬁle is extrapolated into the multiple-image region. The WL(i.e., ﬁlament + cluster core) and overcome the mass-sheet degen- mass thus obtained for the cluster core is MWL (R < 500 kpc) =eracy, we compare the weak-lensing mass obtained for the cluster (1.04 ± 0.08) 1015 h−1 M⊙ in excellent agreement with the value 74core with the technique described in Sect. 4, with the strong lensing measured by Limousin et al. (2012). We also measure MWL (R <(SL) results from Limousin et al. (2012). 350 kpc) = (5.10 ± 0.54) 1014 h−1 M⊙ , in slight disagreement with 74 the result reported by Zitrin et al. (2009). But the excellent agree- ment at larger radii between strong- and weak-lensing results with-5.2.1 Cluster Core out any adjustments validates our redshift distribution for the back-Limousin et al. (2012) inferred a parametric mass model for the ground sources, and our new reconstruction method.core of MACSJ0717.5+3745 using strong-lensing (SL) constraints, Figure 9 compares the mass contours from the two diﬀerentspeciﬁcally 15 multiple-image systems identiﬁed from multi-color gravitational-lensing analyses for the core of MACSJ0717.5+3745data within a single HST/ACS tile. Spectroscopic follow up of and illustrates the remarkable agreement between these totally in-the lensed features allowed the determination of a well calibrated dependent measurements. Our WL analysis requires a bi-modalmass model. The cyan contours in Fig. 9 show the mass dis- mass concentration which coincides with the two main concentra-tribution obtained from their analysis. Four mass components, tions inferred by the SL analysis of Limousin et al. (2012).associated with the main light components, are needed to sat-isfy the observational constraints. The cluster mass reported byLimousin et al. (2012) for the region covered by a single ACS 5.2.2 Detection of a ﬁlamentary structureﬁeld-of-view is MSL (R < 500 kpc) = (1.06 ± 0.03) 1015 h−1 M⊙ 74where the cluster centre is taken to be at the position quoted be- Figure 10 shows the mass map obtained for the whole HST/ACSfore (07:17:30.025 +37:45:18.58). This position was adopted as mosaic using the modeling and optimization method described